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February 2014

Spotlight Summary by Morten Bache

In striving to understand nonlinear optics under extreme conditions, a significant amount of effort has historically been put into casting Maxwell’s governing equations into forms that not only can model the pulse propagation with high accuracy but also shed some insight into the physics at the same time. The photonic-crystal fiber (PCF) has pushed some boundaries in this direction for waveguided interaction, in particular in the ongoing effort to understand the supercontinuum generation process in details. On the other side a parallel race has forced researchers to create evermore complex numerical models to understand how filamentation occurs in bulk media. The current consensus of this extreme event is that it occurs when an intense laser pulse collapses due to the Kerr lens effect (beam self-focusing), only to reach such high intensities that it starts to create photo-ionization of the material, and the created plasma acts as a self-defocusing lens, thereby counteracting the collapse and eventually stabilizing the filament.

While the waveguide case relies on a transverse modal expansion and thereby a considerable reduction in numerical simulation time as the diffraction term is avoided, the filamentation case will require much more extensive computational effort as space-time diffraction must be modeled. So what happens when the waveguide cases reach the peak powers needed for self-focusing effects to occur? Do we need to abandon the speedy modal version and turn to the slow modeling of the diffraction term? In this article, Tani et al. have been asking these questions themselves. Working with a gas-filled hollow-core PCF with a kagomé shaped cladding, they develop a carrier-resolved model where the multi-mode nature of the waveguide is taken into account along with third-order nonlinearity and ionization effects. Even if a convenient modal expansion that separates the carrier-resolved electric field from the transverse modes is used to reduce the computational costs, the ionization term turns out to require a full spatially resolved electrical field: this is calculated in each numerical propagation step from combining the waveguide modes and the electric field at that position.

This hybrid method is then used to model an experiment where an Ar-filled kagomé PCF is pumped at 800 nm, and where the multi-mode coupling results in soliton-induced dispersive-wave formation in the higher-order modes. They also use the model to verify some of the recent experimental results in this kagomé PCF, such as UV third-harmonic generation as well as showers of few-femtosecond solitons generated from extreme modulational instability. Especially the latter case now becomes interesting, because the new model provides some critical insight into the observed results: the simulations show that the shower of few-femtosecond solitons drives strong nonlinear modal coupling to dispersive waves in higher-order modes. This in turn leads to a sort of self-focusing effect, as a narrower total beam profile is observed from the numerics; such a waveguide self-focusing effect has previously been explained as coupling from the fundamental mode to higher-order modes with narrower mode profiles, thus explaining how the total observed mode profile becomes narrower. However, akin to the bulk case, the ionization term kicks in to create a self-defocusing effect, and as a net result the total beam transverse profile is predicted to remain constant. Ionization therefore prevents self-focusing, and this explains why they observed no beam narrowing in their experiment. Instead the result indicates a new waveguide-based filamentation process. Exactly how the self-defocusing can be understood in terms of ionization coupling to the modal contributions to the total transverse field is left open to be explained.